Front-type solutions of fractional Allen–Cahn equation

Super-diffusive front dynamics have been analysed via a fractional analogue of the Allen–Cahn equation. One-dimensional kink shape and such characteristics as slope at origin and domain wall dynamics have been computed numerically and satisfactorily approximated by variational techniques for a set of anomaly exponents 1<γ<21<γ<2. The dynamics of a two-dimensional curved front has been considered. Also, the time dependence of coarsening rates during the various evolution stages was analysed in one and two spatial dimensions.